Symmetry computation and reduction of a wave model in equation id-i-eq1"> equation-source format-t-e-x" xmlns:search="http://marklogic.com/appservices/search">\(\mathbf{2}+\mathbf{1}\) dimensions
We present the iterative classical point symmetry analysis of a shallow water wave equation in \(2+1\) dimensions and that of its corresponding nonisospectral, two-component Lax pair. A few reductions arise and are identified with celebrate equations in the Physics and Mathematics literature of nonlinear waves. We pay particular attention to the isospectral or nonisospectral nature of the reduced spectral problems.